You’ve come up with a few minor challenges with vouchers for public schools, but you ignore the BIGGEST problem we have with our public schools: they are doing a terrible job of educating kids. The majority can’t read or do basic math at grade level! They graduate not knowing when the Civil War was, where Canada is on a map, or how to figure out change from a $20 bill.
And your worry is: what if my kid (or anyone’s kid) isn’t smart enough to get into the private school they want? Well, then you have tiers of private schools: a tough one for the bright kids, and an average one for the average kids. That would be a GOOD thing: our most promising youth will not be held back by dumbed-down classes.
And finally, regarding your statement that you don’t want to pay to send other people’s kids to private: we’re already spending $20,000 a year per student for a horrible public education. We simply allot that money to be used for private.